Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C16 · Schur multiplier (H2) = C22×C8 |
| direct product | C2×C8×C67⋊C16 |
| derived, Sylow | C67 ⋊ C2×C8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C82 | D67 |
| commutator, hypocenter | C67 | C2×C8×C16 |
| Frattini | C4×C8 | C22×D67 |
| Fitting | C2×C82×C67 | C2 |
| socle, prime radical | C23×C67 | C4×C8 |
| cosocle | C4×C8×C67 | C23 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2×C82 | |
398 conjugacy classes of subgroups; only the 339 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 339 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 17152 |
4480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 78540);